Value-at-Risk

In actuarial applications, an important focus is on developing loss distributions for insurance products. It is also critical to employ risk measures to evaluate the exposure to risk. This post provides practice problems on two risk measures that are useful from an actuarial perspective. They are: value-at-risk (VaR) and tail-value-at-risk (TVaR).

Practice problems in this post are to reinforce the concepts of VaR and TVaR discussed in this blog post in a companion blog.

Most of the practice problems refer to parametric distributions highlighted in a catalog for continuous parametric models.

Losses follow a mixture of two exponential distributions with equal weights where one exponential distribution has mean 10 and the other has mean 20. Evaluate the value-at-risk and the tail-value-at-risk at the 95% security level.

Practice Problem 10-H

Losses follow a mixture of two Pareto distributions with equal weights where one Pareto distribution has shape parameter and scale parameter and the other has shape parameter and scale parameter . Evaluate the value-at-risk and the tail-value-at-risk at the 99% security level.

Practice Problem 10-I

Losses follow a Weibull distribution with parameters and . Determine the value-at-risk at the security level 99.5%.

Practice Problem 10-J

Losses follow an inverse Pareto distribution with parameters and . Determine the value-at-risk at the security level 99%.